Two mechanisms have been shown to be particularly important in influencing the ability of a group to engage in effective collective action: punishment and reputation. The former can be described as people willing to sustain an individual cost to punish behaviour that they find inappropriate [1]}. Experiments [2]}, [3]} have found that pro-social punishment (the punishment of a defector by a cooperator) – whose emergence has been linked to the possibility to abstain from participation [4]} – can sustain cooperation in iterated games. More recently however, the positive role of punishment has been criticised, as substantial levels of anti-social punishment (the punishment of cooperators by defectors) have been observed in experiments [5]}, [6]}, [7]}. Although second-order free-riding on anti-social punishment can restore the effectiveness of pro-social punishment in the absence of loners [8]}, allowing this type of punishment significantly reduces cooperation, and re-establishes the rock–paper–scissor type of dynamics among strategies [7]} in the OPGG. Importantly, [7]} show that the strategy of opting out of interactions, combined with a world in which anyone can punish anyone, does not result in any meaningful increase in cooperation. Crucially, it is not the presence of loners that harms cooperation, but the possibility to punish them. Indeed, if loners are shielded from punishment, [11]} show that cooperators that punish pro-socially prevail, even when anti-social punishment is available. Just like anti-social punishment, anti-social pool rewarding (where agents of some type contribute towards rewarding others of their own type) also destabilises cooperation in fully-mixed populations [12]} but not structured populations [13]}.
